Several websites define an ambidentate ligand as being monodentate. What about a ligand with say 3 atoms that can act as donor atoms, but due to the sterics of the ligand, only any two atoms can coordinate bond to an acceptor at any one time?
When a ligand has multiple donor sites, but uses only say $x$ of them at a particular time, then it's called ambidentate ligand. However, if it uses different number of sites in different compounds (say $x$ in one and $y$ in the other where $x\ne y$), then flexidentate is a more appropriate term as said in the other answer. But this doesn't mean all ambidentate ligands are monodentate.
For example, dithiooxalate is bidentate and ambidentate:
This example is from the book Concise Inorganic Chemistry by J.D. Lee (Adapted by Sudarsan Guha).
If the ligand has 3 donor sites and it is able to show multiple denticity in different compounds, then it will be called as flexidentate ligand. But as per your question, if it is only showing denticity of 2 only it will be called as bidentate ligand.
Actually, this concept arose when arguments started for selecting donor sites for the " monodentate ligands " which were always showing denticity of only 1 in all of its compounds instead they had multiple donor sites.
This ambidentate case arises when a ligand can't use its two donor sites simultaneously due to steric hindurence caused due to small distance between them and when the distance between the two donor sites is more, then the ligand now is able to bond with the metal using its multiple sites making it a multidentate ligand.